Upgrade to MySQL version 5.5? If so. It is not in the synaptics package manger.
marked as duplicate by fossfreedom♦, Jorge Castro, ajmitch, Oli♦ Nov 7 '11 at 23:26
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
I think, you'll have to compile it from source: MySQL Download page
You eventually can convert an RPM package to a deb package (there's a tool named "alien" for that), but you don't want to do that.